A continuous field of C*-algebras and the tangent groupoid for manifolds with boundary

摘要

For a smooth manifold X with boundary we construct a semi-groupoid T-X and a continuous field C-r*(T-X) of C*-algebras which extend Connes' construction of the tangent groupoid. We show the as ymptotic multiplicativity of h-scaled truncated pseudodifferential operators with smoothing symbols and compute the K-theory of the associated symbol algebra. (C) 2005 Elsevier Inc. All rights reserved.